Problem: Simplify the following expression: $\dfrac{96n^3}{12n}$ You can assume $n \neq 0$.
$ \dfrac{96n^3}{12n} = \dfrac{96}{12} \cdot \dfrac{n^3}{n} $ To simplify $\frac{96}{12}$ , find the greatest common factor (GCD) of $96$ and $12$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $12 = 2 \cdot 2 \cdot 3$ $ \mbox{GCD}(96, 12) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{96}{12} \cdot \dfrac{n^3}{n} = \dfrac{12 \cdot 8}{12 \cdot 1} \cdot \dfrac{n^3}{n} $ $\phantom{ \dfrac{96}{12} \cdot \dfrac{3}{1}} = 8 \cdot \dfrac{n^3}{n} $ $ \dfrac{n^3}{n} = \dfrac{n \cdot n \cdot n}{n} = n^2 $ $ 8 \cdot n^2 = 8n^2 $